What really happens between Amu and Ikuto in Shugo Chara?

First, because his key(the dumpty key) matches her lock (the humpty lock).

Also, because she does what he can't. ( Heal heart eggs; is nice & kind..etc...) And She seemed to be the only one who understands his feelings sometimes. Also, he liked how Amu react whenever he teased her. She seems to be the only one who can free him or find the embryo. ^^ hope it helps.